MEASURED MIMO CAPACITY ENHANCEMENT IN CORRELATED

LOS INDOOR CHANNELS VIA OPTIMIZED ANTENNA SETUPS

Andreas Knopp, Mohamed Chouayakh, Robert Schwarz and Berthold Lankl

Department of Electrical and Electronics Engineering, Institute for Communications Engineering,

Munich University of the Federal Armed Forces, 85579 Neubiberg, Germany

Keywords:

MIMO techniques, indoor channel measurements, channel capacity, correlated channels, Line-Of-Sight.

Abstract:

Our premise in this paper is to investigate the available channel capacity of MIMO systems in correlated

transmission channels for various antenna arrangements differing in their suitability in order to construct high -

rank LOS channels. Hence, a measurement campaign with a fast 5×5 - MIMO channelsounder was carried out

in a typical, medium - scale, in - room ofﬁce scenario giving the opportunity to virtually evaluate the channel

capacities for arbitrary M × N - MIMO systems ({M, N} ≤ 5) by antenna selection and combination. We

use linear antenna arrays and vary their initial antenna spacings and orientations relative to each other which

coincides with LOS channels of varying rank. In the sequel the measured capacities are compared giving an

idea on the usefulness of the high - rank LOS channel construction in the presence of strong reﬂections. For

our purpose we introduce an appropriate power normalization of the channel transfer matrix to exclude further

effects on the capacity, as for example SNR variations due to varying transmitter - receiver distances, and only

concentrate on the phase angle relations within the matrix. The results show a measurable beneﬁt in channel

capacity when such optimization and normalization is performed, especially for small antenna numbers.

1 INTRODUCTION

Multiple Input - Multiple Output (MIMO) transmis-

sion systems promise high channel capacity gains

and reliability improvements for ﬁxed bandwidth and

transmit power (Telatar, 1995),(Foschini and Gans,

1998). In the context of the system design it is in-

evitable to be able of predicting the accessible chan-

nel capacity. Especially indoor transmission channels

and as a subgroup in-room channels, where transmit-

ter (Tx) as well as receiver (Rx) are located within the

same room, are totally different from common statis-

tical modelling approaches due to their strong Line

- Of - Sight (LOS) signal component in coincidence

with low mobility. In the narrowband case such cor-

related channels have been shown to typically pro-

vide only low MIMO outage capacities, particularly

for small antenna spacings relative to the Tx - Rx

distance (Vucetic and Yuan, 2003), (Molisch, 2005).

Contrarily, theory offers the possibility to enhance

the MIMO capacity of correlated channels by adapted

antenna arrangements that are suitable for construct-

ing high - rank LOS channels, e.g. (Bohagen et al.,

2005). These approaches explore full MIMO capac-

ity for ﬁxed antenna positions as long as there are no

reﬂected waves impinging at the Rx - two conditions

that are hardly fulﬁlled in practice. On the one hand it

is impossible to optimize the antenna setups for every

position in the room and on the other hand the LOS

signal never exists without reﬂections. Nevertheless

we consider the LOS component being carrying most

of the signal power. Therefore optimally chosen an-

tenna setups which nearly can exploit the LOS com-

ponent all over a particular room area should help

to improve the channel’s outage capacity even in the

presence of reﬂections. This approach will particu-

larly be probed in the sequel. Hence, in section 2 a

channel description is provided and the capacity cal-

culation is described. In section 3 we present our re-

sults from measurements as well as some preliminary

insights derived from simulation. Last, we conclude

the paper in section 4.

2 CHANNEL MODEL AND

CAPACITY CALCULATION

General presumptions on the channel: In the con-

text of MIMO applications and their capacity the in-

187

Knopp A., Chouayakh M., Schwarz R. and Lankl B. (2006).

MEASURED MIMO CAPACITY ENHANCEMENT IN CORRELATED LOS INDOOR CHANNELS VIA OPTIMIZED ANTENNA SETUPS.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 187-193

Copyright

c

SciTePress

door WLAN channel is commonly statistically mod-

elled, where the modelling approaches concentrate on

the NLOS transmission paths forming numerous and

variously reﬂected waves (”rich scattering”). To ful-

ﬁll these assumptions the LOS component must be

distinctly attenuated by shadowing effects or when as-

suming high reﬂection factors ξ

2

≈ 1 the path lengths

of the reﬂected waves must be in the range of the LOS

path length. In this case the propagation loss of direct

and reﬂected signal components range in the same or-

der of magnitude and hence the reﬂection’s impact

rises. Usually those assumptions are less valid for in

- room scenarios than for outdoor transmission with

large distances between Tx and Rx. Therefore a sim-

ilar modelling strategy is regularly performed in mo-

bile communications. When in addition narrow trans-

mission bandwidths are presumed the channel can be

treated ﬂat and information is provided only on the

magnitude level distribution which especially in the

case of high mobility can be modelled by a Rayleigh

process (Paetzold, 2002). In this case the entries of

the channel transfer matrix are assumed to be uncor-

related, zero mean, i.i.d. complex Gaussian random

variables, a case which describes a convenient trans-

mission channel for MIMO applications as the ex-

pected value of its capacity is high (Telatar, 1995) as

long as the receive signal correlation is kept low. Ac-

cording to (Jakes, 1974) the latter condition can be

achieved by antenna spacings of at least about half -

wavelength (λ/2) what therefore has become a com-

mon design issue for MIMO antenna arrays. When

the direct LOS signal component gets present this fact

can be incorporated leading to the well known Rice

propagation model (Paetzold, 2002). This statistical

approach is widely used when discussing early indoor

transmission systems and it is included in the popu-

lar, cluster based channel model introduced by Saleh

(Saleh and Valenzuela, 1987).

Contrarily, in the case of the in - room propagation

scenario discussed in the sequel a dominant LOS sig-

nal component that carries most of the energy is al-

ways present which in the consequence leads to cor-

related signals at the receiver inputs. Of course also in

indoor scenarios the LOS signal component ist some-

times obstructed and therefore diffracted by objects

but it is known from the theory of diffraction that no

signiﬁcant losses arise as long as the obstructing ob-

stacle’s size stays below the ﬁrst Fresnel zone’s di-

mension. For a typical WLAN center frequency of 2.4

GHz and distances of 2 m and 3 m between the obsta-

cle and the Tx and Rx, respectively, the size of the ﬁrst

Fresnel zone is about 80 cm in diameter which is large

compared to typical furniture or persons. Besides, one

set of antennas (Tx or Rx) is typically mounted at the

ceiling which distinctly reduces the risk of obstruc-

tion. In these scenarios the simple approach of a λ/2

antenna spacing is no longer sufﬁcient as it theoret-

ically can not exploit the maximum MIMO capacity

with respect to LOS. By geometrically optimizing the

antennas’ positions and spacings at Tx as well as Rx

resulting in proper phase angle relations among the

entries of the channel transfer matrix, it is possible to

make accessible the maximum MIMO capacity even

in the case of correlated channels. Coinciding it is

inevitable that the LOS signal component never ex-

ists without reﬂections which can hardly be included

in any strategy of constructing high - rank channel

transfer matrices. Obviously this effect gets more em-

inent when the power contributed by reﬂections rises

as it is the case for declining room dimensions. Be-

fore we answer the question to what extent the high

- rank LOS channel construction enhances the capac-

ity in such real - world scenarios the theoretic back-

ground in terms of channel modelling and capacity

calculation is summarized.

Capacity calculation: Contingent upon the consid-

ered transmission bandwidth our measurements cover

the case of nearly frequency ﬂat channels. Neverthe-

less, a frequency selective channel model should be

assumed because it also includes the frequency ﬂat

channel as a special case and it is necessary for our

way of evaluating the measured results as it will be ex-

plained in the sequel. According to our presumptions

mentioned above we consider the following, widely

deterministic description of the MIMO transmission

channel. For a single input - single output (SISO) fre-

quency selective, deterministic transmission channel

the equivalent baseband channel transfer function for

the time invariant case is given by

H(f) =

K−1

X

k=0

a

k

e

−j2πf τ

k

=

K−1

X

k=0

a

k

e

−j2π

L

k

λ

, (1)

where the sum is evaluated over the K different trans-

mission paths consisting of K − 1 reﬂected signal

parts and the LOS signal component is incorporated

by the index k = 0. The complex amplitude factor

a

k

includes the phase information φ, the path - loss

as well as the power - loss due to the reﬂection fac-

tor ξ

2

, i.e. a

k

=

ξλ

4π L

k

e

jφ

. The time τ

k

denotes the

signal part’s delay for the particular transmission path

which is clearly linked to its path length L

k

by the

speed of light c

0

, i.e. τ

k

= L

k

/c

0

. The right part of

the equation additionally introduces H(f ) depending

on the wavelength λ. For a non - mobile scenario a

k

and τ

k

are mainly constituted by the location’s geom-

etry, i.e. primarily by the Tx’s and Rx’s positioning

within the room as well as their arrangement in rela-

tion to the main reﬂection layers like walls, bottom,

ceiling or large scale objects. With increasing mobil-

ity it is more and more appropriate for the channel

to be modelled by some statistical process. In the ob-

served scenarios described in this paper the amount of

WINSYS 2006 - INTERNATIONAL CONFERENCE ON WIRELESS INFORMATION NETWORKS AND SYSTEMS

188

mobility is kept low and therefore no statistical mod-

elling over time is performed.

Applying equation (1) to the MIMO case, for a time

invariant frequency selective M × N - MIMO sys-

tem consisting of N transmit and M receive antennas

the vector of receive signals y(t) ∈ C

M×1

is calcu-

lated by an inverse Fourier transform of the spectrum

of the transmit signal vector X(f) ∈ C

N×1

multi-

plied by the frequency selective channel transfer ma-

trix H(f ) ∈ C

M×N

, i.e.

Y (f ) = H(f) X(f ) + Υ(f), (2)

where Υ(f) ∈ C

M×1

denotes the spectral vector of

the additive noise η(t). The noise is assumed to be

zero-mean complex Gaussian with covariance matrix

R

η

= E[ηη

H

] = σ

2

η

I

M

, where I

M

∈ C

M×M

de-

notes the identity matrix and σ

2

η

is the noise power

at each receive antenna. Here each entry H

mn

(f) in

H(f) has the structure of equation (1) whereas the

values K and hence, a

k

and τ

k

differ.

According to (Telatar, 1995) and (Foschini and Gans,

1998) when uncorrelated transmit signals are pre-

sumed the time invariant channel capacity for a fre-

quency selective MIMO - channel in the absence of

channel knowledge at the transmitter is calculated

from

C =

B

log

2

det

I

M

+

σ

2

x

σ

2

η

H(f)H

H

(f) df, (3)

where B denotes the transmission bandwidth, I

M

∈

C

M×M

is the identity matrix, σ

2

x

denotes the mean

transmit power that is allocated to each transmit an-

tenna. Furthermore (.)

H

abbreviates the complex con-

jugate transpose. When the overall bandwidth is par-

titioned into sufﬁciently narrow, say S, segments each

segment can be treated frequency ﬂat and the integral

of equation (3) reduces to a sum over the segments’

capacity contributions, i.e.

C =

B

S

S

s=1

log

2

det

I

M

+

σ

2

x

σ

2

η

H[f

s

]H

H

[f

s

] . (4)

Equation (4) is used for the capacity calculation from

measured data samples in section 3. From equations

(3) and (4) it can be observed that the capacity is op-

timized by ﬁnding the optimal matrix entries in the

channel transfer matrix H(f ) dependent upon the fre-

quency f. When only a LOS signal component is

present this can be resolved by geometrically optimiz-

ing the antennas’ position such that a high - rank chan-

nel transfer matrix is obtained. Several early sugges-

tions from different authors, e.g. (Driessen and Fos-

chini, 1999), were made for the construction of these

channels but all of them suffer from the drawback that

due to mathematical restrictions they are limited to

only a small number of antennas. Furthermore the re-

sulting geometric setups are often improper for prac-

tical applications as in the consequence the antennas

have to be positioned far from each other all over the

room. A recent and most general solution which over-

comes the drawback of limited antenna numbers can

be found in (Bohagen et al., 2005) where the authors

present a strategy for the design of linear antenna ar-

rays which under weak presumptions leads to a chan-

nel transfer matrix close to full - rank.

Additionally a very simple example which illustrates

a possibility to optimize the channel capacity even in

deterministic correlated MIMO channels in the case

of a ﬂat fading for a ﬁxed location of Tx and Rx can

be found in (Knopp et al., 2005). Of course in prac-

tice such optimization would have to be performed

for every possible location what is far from realizabil-

ity. Despite this fact the simple example and further

analysis that have been performed in advance of our

measurements, e.g. the deviation of the pure LOS

capacity across a room of particular size for various

antenna spacings, suggest that it is reasonable to gen-

erally enlarge the antenna spacings in order to better

exploit the strong LOS signal component for possi-

bly large areas of a room without taking into account

reﬂections. The arising question to what extent the

antenna setup’s simpliﬁed optimization for LOS via

enlarged but ﬁxed antenna spacings all over the room

even in conjunction with reﬂections stays still prof-

itable is discussed in section 3.

3 RESULTS

3.1 Scenario Description and

Method of Measurement

For the channel measurements we used a 5×5 MIMO

channelsounder with a bandwidth of 80 MHz at a

carrier frequency of 2.45 GHz endowed with λ/2

dipole antenna arrays positioned as equidistantly -

spaced uniform linear arrays (ULAs). The maxi-

mum bandwidth ranges some factor above the typ-

ical bandwidths proposed for current and future in-

door applications and hence, achieves a higher time

resolution. The channel information was collected

by sequentially deriving the entries of the channel

transfer matrix, i.e. by collecting the complex base-

band channel impulse responses (CIRs) and channel

transfer functions (CTFs). A Perfect Squares - Mini-

mum Phase (PS - MP) CAZAC sequence (Linde and

Roehrs, 1993) was used as pilot signal, a discrete

sequence with a frequency ﬂat power spectrum and

therefore a perfectly zero autocorrelation for differ-

ent time instances. We used 196 pilot symbols and

due to our sampling rate of 100 MHz we achieved

a frequency resolution of 510 kHz (196 · 510 kHz

= 100 MHz), but for the capacity evaluation we re-

duced the considered bandwidth off line to 80 MHz

MEASURED MIMO CAPACITY ENHANCEMENT IN CORRELATED LOS INDOOR CHANNELS VIA OPTIMIZED

ANTENNA SETUPS

189

by digital ﬁltering. The measurement of one complete

channel matrix consisting of 25 entries took about

160 µs. This measurement time is short enough by

far to consider the channel invariant during that time,

especially in the chosen scenarios with low mobility

and it is much faster than even a single SISO network

- analyser measurement which typically takes around

100 ms. A further advantage of the system is the fact

that after measuring the 25 CIRs we are able to arbi-

trarily combine them in off - line mode and virtually

built up different MIMO systems by antenna selection

from the measured data, in fact

5

M

5

N

combinations

are possible for an M × N MIMO system.

The measurements were taken within a modern ofﬁce

building constructed from steel and glass. We chose

a typical medium - scale ofﬁce or laboratory scenario

which is depicted in detail in ﬁgure 1 providing all

necessary information on the materials, dimensions

and arrangements of the walls and the most impor-

tant furniture. The room was equipped by typical of-

Figure 1: Schematics of the measured location.

ﬁce working desks, i.e. wooden desks and chairs with

metal legs. Additionally a metal bar was placed in the

center of the room dealing as a divider. The Tx was

arranged on top of that divider at height 2.25 m what

supposes that in the context of in - room scenarios

the Tx might reasonably be placed near the ceiling to

guarantee a LOS link for every receiver position. The

Tx position was kept ﬁxed while the Rx was moved at

typical working desk hight in two dimensions across

the room along a grid. During one complete grid mea-

surement the relative positions of the Tx and Rx an-

tenna array were not changed and either broadside or

perpendicular (see ﬁg. 1). The mobility was kept low

and therefore the statistical analysis of the measured

data was performed in the spatial domain treating the

Rx position as a random variable. The statistic was

expanded by an additional evaluation of the 196 fre-

quency segments of bandwidth 510 kHz which our

sampled transfer function was partitioned into. We as-

sumed every frequency segment being a realization of

a possible narrow band transmission channel out of 80

MHz / 510 kHz = 156 possible transmission channels

around the carrier of 2.45 GHz. From equation (1) it

becomes obvious that the relation L

k

/λ is the key pa-

rameter for the CTF’s phase angle as well as its path

- loss. Changing the Tx - Rx distances the value L

k

is changed resulting in a different CTF. Changing the

carrier frequency the wavelength λ is changed what

also alters the CTF. Interpreting the variation of L

k

/λ

due to the change of λ as if λ was kept ﬁxed and L

k

was altered instead, the statistical evaluation of dif-

ferent frequency segments which are placed close to

each other around the carrier can be interpreted as vir-

tually moving the Rx within a small area. This strat-

egy provides the possibility to enlarge our spatial sta-

tistics.

3.2 Mimo SNR Deﬁnition and

Capacity Normalization

A crucial aspect when evaluating measured channel

transfer functions in terms of the channel capacity is

the deﬁnition of the signal to noise ratio in equation

(3). Generally, we suggest a deﬁnition that best rep-

resents the physical reality of transmission systems

with respect to their degrees of freedom for the user.

Those are mainly the transmit power per transmit an-

tenna σ

2

x

and the noise power per receive antenna σ

2

η

as the latter includes the receiver noise ﬁgure which

depends on the chosen hardware. Of course with that

deﬁnition the ratio σ

2

x

/σ

2

η

does not meet the com-

monly used SNR deﬁnition ρ which describes the re-

ceive signal to noise ratio at the receiver input, but ρ

clearly emanates from σ

2

x

/σ

2

η

if it is multiplied by the

channel’s path loss ζ

2

, i.e. ρ = σ

2

x

/σ

2

η

· ζ

2

. In our

deﬁnition ζ

2

is completely incorporated in the chan-

nel transfer matrix which causes ρ at the receiver in-

put being dependent upon the distance between Tx

and Rx as well as the number and power of imping-

ing waves. This approach does best represent phys-

ical reality as it focusses on the true capacity avail-

able in practice including all the relevant effects. To

give an example: if the commonly investigated Non

- LOS Rayleigh ﬂat fading channel for a given value

of ρ (which again denotes the resulting SNR at the re-

ceiver input) is considered, the capacity will be com-

paratively close to its maximum for that ρ. If now

a strong LOS signal component is brought into the

scene the value of ρ will be distinctly higher what

rises the true channel capacity. If the rank of the

channel transfer matrix for certain geometric antenna

arrangements is observed, it will be close to rank = 1

for the LOS case and close to full - rank without the

LOS. Nevertheless, if one concludes from the obser-

vation of the channels’ ranks that the one with LOS

WINSYS 2006 - INTERNATIONAL CONFERENCE ON WIRELESS INFORMATION NETWORKS AND SYSTEMS

190

present is worse for MIMO applications, this conclu-

sion in most cases will be totally wrong as the SNR

gain is ignored. The risk of such misinterpretation es-

pecially rises if the comparison of the two channels

is performed by simply substituting ρ for σ

2

x

/σ

2

η

and

in addition normalizing the channel transfer matrix by

an appropriate matrix norm to unit power for compen-

sation, i.e. eliminating the path loss from the channel.

If now the two power - normalized channels are com-

pared for the same value of ρ, the Non - LOS chan-

nel will clearly outperform the LOS channel, a result

which is far from the truth in most cases. Hence, we

propose to avoid any normalization to evaluate dif-

ferent channels with respect to their effective channel

capacity.

Nevertheless, if one’s interest focusses on certain ef-

fects and their inﬂuence on the capacity it might be

reasonable to eliminate all the further effects that af-

fect the capacity besides. In this paper we concretely

investigate the antenna arrangement’s impact on the

channel capacity what rather means that we want to

ﬁnd out how different antenna spacings can inﬂuence

the channel matrix’ rank in the presence of reﬂec-

tions. We perform a spatial statistics what coincides

with varying Tx - Rx distances. As we do not want to

take into account the variation of ρ due to those dis-

tance changes we therefore replace σ

2

x

/σ

2

η

in equa-

tion (3) by ρ and keep its value ﬁxed (in the sequel

it is set to ρ = 30 dB), while we eliminate the path

loss from the channel transfer matrix by normalizing

it to unit power using the Frobenius matrix norm, i.e.

||H||

2

F

= 1. This norm simply sums up the matrix

entries’ power and normalizes by that sum. The strat-

egy is appropriate for our investigations but the reader

should be aware of the given presumptions when in-

terpreting the results. To give a physical interpreta-

tion, the used normalization is equivalent to perma-

nently adjusting the Tx power in order to keep the Rx

input power and therefore ρ ﬁxed independently from

the channel.

3.3 Evaluation of the Results

Preliminary simulations: To develop an idea of the

reﬂections’ impact on the outage capacity (OC)

1

be-

fore presenting our measured results we provide re-

sults from simulation. We simulatively obtained ca-

pacity cumulative distribution functions (CDFs) for a

room with identic dimensions as our measurement lo-

cation while considering the direct (LOS) signal com-

ponent as well as the reﬂections from all the surround-

ing walls, the bottom and the ceiling. In the simpli-

ﬁed simulation we included single, double, triple and

1

the x % outage capacity describes the capacity value

which is NOT exceeded with a probability of x % (Vucetic

and Yuan, 2003)

quadruple reﬂections and calculated them by means

from geometric optics using a spherical wave model

but ignored further effects like diffraction, scattering

and transmission through objects. The Tx was placed

in the center of the room and the Rx was moved, both

at a height of 1.5 m. The reﬂection factor was set to

0.3 what corresponds to an amplitude - loss of 10.5

dB, which describes a typical but comparatively high

reﬂection factor for indoor materials what in the con-

sequence slightly overestimates the reﬂection’s power

marking a worse case than practically expected. Sim-

ilar to our measurements and in accordance to the

description of subsection 3.1 the simulation was per-

formed over a bandwidth of 80 MHz formed by nar-

rowband frequency segments of 500 kHz and the re-

sults were statistically evaluated over a spatial grid as

well as over those frequency segments. The capacities

were calculated according to equation (4). Besides

the normalization of the channel transfer matrix we

furthermore normalized the capacity by min{M, N}

which is equivalent to the maximum linear capacity

increase of an M × N - MIMO system. This normal-

ization leads to capacities which are approximately

independent from the number of antennas and there-

fore also eases comparability as the capacity CDFs lie

within similar ranges of magnitude. The results for a

2 × 2 - MIMO system with different antenna spacings

(equally chosen at Tx and Rx) are depicted in ﬁgure

2. For both antenna spacings 5 curves can be observed

Figure 2: Simulated C-CDFs for different antenna spacings.

differing in the considered number of reﬂections. The

legend entry ”up to 2 reﬂections” for example denotes

the case of considering the LOS signal part and all

reﬂected waves which were reﬂected twice at maxi-

mum. For the usually chosen λ/2 spacing the CDF

considering only the LOS signal part clearly indicates

a very low capacity with low spatial variations what

can be seen from the steepness of the curve. This can

be understood from the fact that the channel trans-

MEASURED MIMO CAPACITY ENHANCEMENT IN CORRELATED LOS INDOOR CHANNELS VIA OPTIMIZED

ANTENNA SETUPS

191

fer matrix is close to rank = 1 for that small antenna

spacings nearly all over the room. Obviously when

reﬂections are included the capacity increases, the 50

% OC for example is increased by about 35 % com-

pared to its minimum for the 2×2 - MIMO system but

the 10 % OC only slightly increases by about 15 %.

Obviously the reﬂections help to increase the OCs by

enhancing the channel transfer matrix’ rank but com-

pared to the case of a Rayleigh fading channel of iden-

tical power the capacity stays still low.

Contrarily, when the antenna spacing is enlarged what

according to the example presented in the previous

section coincides with enhanced utilization of the

LOS component in terms of MIMO the 10 % OC for

the pure LOS is increased already by over 20 % and

the 50 % OC is even increased by about 72 %. Con-

sidering the reﬂections in addition the 10 % OC is

further increased by 18 % while the 50 % value stays

unchanged compared to the pure LOS case. From

that OC onwards the reﬂections no longer increase

the MIMO gain, contrarily from about the 50 % OC

up they even reduce it. This supports the idea that in

optimally conﬁgured systems with respect to LOS the

reﬂections disturb the well adapted phase angle rela-

tions within the transfer matrix (see (Bohagen et al.,

2005), (Knopp et al., 2005)) and therefore reduce the

capacity although in the simulation only a negligi-

ble reduction can be observed. The low steepness

of the pure LOS CDF in the large antenna spacing

case shows the second problem of the optimization

approach: any optimized antenna spacing only holds

for a certain spatial region and can even correspond to

the worst case outside that region. Therefore the spa-

tial variation of the capacity for a ﬁxed antenna spac-

ing is high. Last, it is observed from the ﬁgure that

in the low capacity case with a LOS channel transfer

matrix close to rank = 1 its rank is already distinctly

increased by only considering single reﬂections and

for the case of double reﬂections a further capacity

increase can be observed. If the LOS signal part is ex-

ploited well the reﬂections’ inﬂuences on the capacity

reduces meaning the better the LOS is exploited the

more the capacity seems to be statistically dominated

by LOS. Generally it appears to be sufﬁcient in terms

of the capacity if triple and quadruple reﬂections are

neglected as their weak power contributions can not

signiﬁcantly change the capacity CDFs.

Measurements: Taking a look at the correspond-

ing capacity CDFs obtained from measured data the

basic results from the preliminary, simpliﬁed simula-

tions are widely conﬁrmed. It must be outlined in ad-

vance that the particular results (especially the mea-

sured values and numbers) are only valid for the cho-

sen antenna spacings which were not particularly op-

timized to maximize the capacity all over the partic-

ular environment. We just used an arbitrary spacing

Figure 3: Measured C-CDFs for various settings.

larger than half - wavelength which was known to de-

liver local capacity maxima in terms of LOS (Knopp

et al., 2005). We not especially tried to ﬁnd the dis-

tinctly best choice with the most capacity maxima for

the range Tx - Rx distances in the investigated room

as we hold the opinion that such strategy is far from

practice due to its complexity. So it is still possible

to discover antenna spacings which even outperform

and further stress the results presented next.

Firstly looking at the curves for the narrowband 2 × 2

- MIMO system it can be observed from ﬁgure 3 that

for larger antenna spacings the 10 % OC for instance

can be increased up to 10 %. In the contrary to the

simulation for the 50 % OC the percentage increase is

not even higher but slightly lower. On the other hand

even in the λ/2 antenna spacing case which is badly

conditioned for LOS the 10 % OC already reaches a

value about 20 % above the simulation. This supports

the assumption of the simpliﬁed simulation model be-

ing not thoroughly sufﬁcient for capacity simulations

as the receive power contributed by reﬂected and scat-

tered waves seems to be higher than the model ex-

pects, say the scattering is somewhat richer than in

the simulation at least in the medium - scale ofﬁce

scenario under investigation due to its well reﬂect-

ing materials. This fact principally has to be regarded

positive for the MIMO channel capacity as the impact

of the LOS - exploitation decreases. Taking a look

at the larger antenna spacings the curves are steeper

in practice than for the larger antenna spacing in the

simulation what states that in the case of nearly opti-

mum antenna spacings with respect to LOS the reﬂec-

tions disturb the phase relations in the channel trans-

fer matrix and reduce the matrix rank as it already

was expected by theory. Hence, for the current sce-

nario the optimization for LOS by choosing larger an-

tenna spacings still enhances the OC whereas the ca-

pacity gain of about 10 % is comparatively low. If

WINSYS 2006 - INTERNATIONAL CONFERENCE ON WIRELESS INFORMATION NETWORKS AND SYSTEMS

192

beyond the spacing enlargement the number of an-

tennas at Rx and Tx is increased the normalized ca-

pacity gain is still observable but slightly decreases

compared to the case of less antennas. The reason is

found from the fact that the higher the antenna num-

ber the less the simpliﬁed approach of larger, equally

chosen antenna spacings ﬁts the optimal conﬁguration

for large areas of the room. So the curves in general

shift closer to the minimum capacity whereas it must

be considered that the real capacity without normal-

ization still gets higher if the number of antennas is

increased

2

. A further result which we obtain from the

curves is the normalized OC increasing for asymmet-

ric MIMO systems with a higher number of receive

antennas as can be seen from the ﬁgure. This effect

comes from the enhanced receive diversity which not

only increases the receive power but also reduces the

capacity’s variation as the correlation of the receive

signals is reduced. The curve steepness generally in-

creases for higher number of antennas showing re-

duced capacity variations. A last modiﬁcation is in-

troduced by changing the antenna arrays’ positioning

towards each other from broadside to perpendicular.

As it was shown in (Knopp et al., 2005) this con-

ﬁguration can hardly exploit the LOS component and

therefore the LOS capacity part stays close to its min-

imum. This conﬁguration is even worse than λ/2 an-

tenna spacing and it is nearly completely independent

from the antenna spacing. This result is widely con-

ﬁrmed by the measurements as the spacing enlarge-

ment hardly provides a capacity improvement. Here

again the antenna setup’s important impact is con-

ﬁrmed. To shortly summarize the results: as a rule of

thumb the measurements suggest to use antenna spac-

ings of a few wavelengths

3

and choose an asymmetric

MIMO system with a higher number of Rx antennas

than Tx antennas.

4 CONCLUSION

In this paper we showed by measurements that the an-

tenna setup’s adjustment at Rx and Tx in order to con-

struct higher - rank LOS channels might be beneﬁcial

in practice. For the sake of simplicity and practical

realizability we only worked with linear antenna ar-

rays and chose a simpliﬁed optimization approach of

changing the antenna spacings and the arrays’ initial

orientation relative to each other and we kept those

parameters ﬁxed for the measurements all over the

room being aware that this proceeding is far from re-

ally optimizing the antenna’s position for every mea-

surement as proposed for example by (Bohagen et al.,

2

remember that our curves in reality have to be multi-

plied by min{M, N}

3

The concrete value is dependent mainly on the dimen-

sion of the room

2005). Despite such simpliﬁcation we clearly could

enhance the channel’s outage capacity even though

we had to cope with strong reﬂections and scatter-

ing effects disturbing the LOS signal part. Hence,

we conclude that optimizing indoor MIMO systems

by measures of low complexity for its powerful LOS

signal component already is an appropriate procedure

to enhance the available channel capacity of those cor-

related transmission channels. We furthermore expect

the enhancing effect being even rising with increasing

room dimensions as the reﬂected waves’ power con-

tribution decreases.

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